Constraints in embryonic development are thought to bias the direction of evolution by making some changes less likely, and others more likely, depending on their consequences on ontogeny. Here, we characterize the constraints acting on genome evolution in vertebrates. We used gene expression data from two vertebrates: zebrafish, using a microarray experiment spanning 14 stages of development, and mouse, using EST counts for 26 stages of development. We show that, in both species, genes expressed early in development (1) have a more dramatic effect of knock-out or mutation and (2) are more likely to revert to single copy after whole genome duplication, relative to genes expressed late. This supports high constraints on early stages of vertebrate development, making them less open to innovations (gene gain or gene loss). Results are robust to different sources of data -- gene expression from microarrays, ESTs, or in situ hybridizations; and mutants from directed KO, transgenic insertions, point mutations, or morpholinos. We determine the pattern of these constraints, which differs from the model used to describe vertebrate morphological conservation ("hourglass" model). While morphological constraints reach a maximum at mid-development (the "phylotypic" stage), genomic constraints appear to decrease in a monotonous manner over developmental time.